Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1403)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=4

http://functions.wolfram.com/07.25.03.1403.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {4, 9/2}, -z] == (14 (6 + 17 z))/(221 z^3) + (1/(1955266560 z^3)) ((-570881115 - 873176220 z + 463276800 z^2 + 846830160 z^3 + 339963360 z^4 + 59886528 z^5 + 5182464 z^6 + 213760 z^7 + 3328 z^8)/ E^z) + (1/(3910533120 z^(7/2))) (Sqrt[Pi] (-172297125 - 1860808950 z - 1654052400 z^2 + 1543782240 z^3 + 1984862880 z^4 + 735134400 z^5 + 124750080 z^6 + 10575360 z^7 + 430848 z^8 + 6656 z^9) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]